Tim Kerins graduated in 2005.
PhD. Thesis Title: Architectures for Cryptography Based on Elliptic Curves
Abstract: Elliptic curve cryptosystems (ECCs) currently o®er more security per key bit than many other public key schemes. A class of related cryptosystems - pairing based cryptosystems - also based on elliptic curves allow identity based encryption where an arbitrary binary string to represent a users public key. At the core of ECCs lies the point multiplication operation, while pairing based cryptosystems often rely the efficient computation of the Tate pairing operation. This thesis is concerned with novel algorithms and architectures for the hardware implementation of these core operations on an elliptic curve over an underlying Galois field.
A new architecture for a Galois field arithmetic processor over GF(pm),p > 2 is described based on the theory of Grobner bases. A flexible ECC processor over GF(2m) is then detailed based on this processor capable of adapting to varying speed/security requirements on the fly. New algorithms and architectures for multiplication and inversion in GF(pm), p > 2 are discussed. In this thesis it is shown that, in certain cases ECC based cryptographic schemes over GF(pm), p > 2 will outperform their GF(2m) counterparts. The Tate pairing is implemented on supersingular elliptic curves over Galois fields of characteristic three. Algorithms for calculation of the Tate pairing are outlined and it is illustrated how this calculation can be efficiently performed in hardware. Two new hardware processors for Tate pairing calculation are described based on Galois field arithmetic over GF(3m).